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Need 6 pages paper. Two files, first file is guidelines, and the top of the guidelines have two links, the first one is guideline example, and second one is example paper. All requirement is in guideline. The second file my textbook, so you also can get some information from our book if you need. Due US pacific time 11/22 night.

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Term Paper Thesis Argumentation 200 Grade Points Due As Assigned Via E-mail Guidelines on Writing a Philosophy Paper: Start by reading the Notre Dame University Guidelines http://www.jimpryor.net/teaching/guidelines/writing.html By Professor Jim Pryor and finally, Professor Peter Horban's "Writing a Philosophy Paper" http://www.sfu.ca/philosophy/resources/writing.html Then, follow these Ten Commandments and everalsting grade salvation shall be thine. While the primary intent for publishing these 'commandments' is to aid your success in my Logic and Critical Thinking courses, anyone can use these steps to formulate a defensable term paper in philosophy. These are NOT mere guidelines for this Critical Thinking and Writing course, however. These are the NECESSARY AND SUFFICIENT CONDITIONS for writing a successful term paper in this course. Since satisfying these necessary and sufficient conditions entails demonstrating the skills of VALID and SOUND reasoning, then many students may well find these 'commandments' useful and productive in writing any paper assigned in your academic life. Be well and prosperous! PART ONE OF YOUR TERM PAPER: VALIDITY 1. THOU SHALT STATE THY THESIS: A philosophy paper begins with the statement of a claim to be defended. This claim is a proposition and constitutes the THESIS of your term paper. The first paragraph of your paper should state clearly what 'thesis' proposition you intend to defend. Example: "Political Science is an oxymoron" Choose a topic from your major academic discipline of study. The example is suitable for a political science major. If you don’t have a major yet, then choose a claim you wish to defend in an area of study interesting to you and where you have sufficient general background knowledge. Example: "There is a high degree of probability that intelligent life exists on other planets in the known universe." Perhaps you want to challenge the views of another thinker. If so, then your thesis statement would read something like this. Example: "I oppose the view held by Gilbert Ryle that states that the term ‘mind’ refers merely to the functions of the brain rather than to some being separate from the brain." Your statement of the claim is your thesis. You will defend this view by advancing a series of reasons called arguments. You may need many sub-arguments in order to get to your main thesis argument. Prepare a bulleted outline of what those arguments will entail. List the kinds of evidence or proof you will need for each argument. Is your argument purely analytical (a priori) like Anselm’s argument for the existence of God? Then you will have no soundness issues to deal with only issues of validity. Or, is your argument concerning some area of practical reasoning (a posteriori) as is in the first example stated above about political science? In that case you will have to deal with both issues of validity and soundness. This outline should be free from mere opinions, beliefs, feelings, hearsay or things you vaguely remember Monica Lewinsky saying in her interview with Barbara Walters on TV. Your outline should ONLY CONTAIN REASONS that support other statements in the outline by logical entailment. 2. THOU SHALT DEFINE ALL THY TERMS: Take each section of your outline and break it down into smaller sections containing premise statements (propositions) that lead to conclusions. List what kind of definitions you intend to employ for the terms in the premises you use for each sub-argument and your main argument. Are your definitions stipulative, lexical, functional, theoretical or some combination thereof? Make careful note of this in your outline. At this stage, be prepared to go through several drafts of your paper before you get to the final version. Three to four drafts are quite to be expected in writing a good philosophy paper, especially if this is your first attempt. Show your drafts to me or to a tutor for comment and suggestions. 3. THOU SHALT STATE THY ARGUMENT IN A VALID FORM: Choose a deductive method of reasoning to compose your arguments. This could be a series of standard form categorical syllogisms where each conclusion serves as the major premise for the succeeding argument until you arrive at the main argument also stated in standard form categorical syllogistic form. Choose one of the 15 Valid Forms. 4. THOU SHALT PROVE YOUR ARGUMENT(S) VALID: Once your argument is formulated using one of the known 15 valid standard form categorical syllogisms you must then prove validity of your argument. You do this by use of a VENN DIAGRAM and The 6 Rules for Validity in Standard Form Categorical Syllogisms. Embed the Venn Diagram for your thesis argument in the body of your text. Parse your argument through each of the 6 Rules. DO NOT FAIL TO DO THIS! If you have mastered these techniques you should have no trouble getting to this point. If you have trouble, see a tutor or bring your work to class for analysis. I’ll be happy to evaluate it with you. PART TWO OF YOUR TERM PAPER: SOUNDNESS 5. THOU SHALT ANALYZE THE SOUNDNESS OF THY ARGUMENT: Once your argument is proven VALID then each of the premises for the main argument must be submitted to inductive analysis to determine their empirical probability. Here you need to state the empirical conditions under which they could be tested. Of course, if your argument contains terms and propositions about those terms that are beyond the realm of empirical proof then you must state why that is the case. Then you must present an 'analytical' proof for your premises. THIS IS A CRUCIAL STEP IN YOUR PAPER. Valid arguments are easy to construct since validity is purely a matter of correct form. Sound arguments, on the other hand, are valid arguments that have all factually true, empirically verifiable, scientifically demonstrable premises to a high degree of probability. If you find that the premises have scientifically weak evidence then you cannot claim soundness for your argument, just weak probability. Empirically weak arguments provide little reason to accept them as factually true. Don’t be shy to come to this conclusion if the evidence warrants it. That’s the point of doing the paper, i.e. to see if valid and sound reasoning can substantiate the truth-claim of your term paper thesis. 6. THOU SHALT SUMMARIZE THY FINDINGS: As a last step in your paper, review where you began, where your inquiry took you and where you concluded. If this process changed your views on the issue underlying your thesis then state the reasons why. If you discover that there is little or no empirical verification for the factual truth of your premises, then say so. If you have come to some original insights about this issue, then state what those insights are. Typically, your summary paragraph will be quite short. 7. THOU SHALT MAKE THY PAPERS printed 6-10 pages in length, double-spaced, spell-checked and grammar-checked documents. Make two copies of your final paper. Keep a backup copy in digital format. 8. THOU SHALT FOLLOW APA (American Psychological Association) style and format for printing your final paper. List all references and resources used according to the APA format. 9. THOU SHALT NOT COVET THY NEIGHBORS WORK. I define plagiarism as submitting the work of another as if it were your own. 10. REMEMBER TO READ THY PAPER ALOUD: Before you hand in your paper READ IT ALOUD to yourself and/or to a kind friend. You will catch last minute mistakes this way as well as enjoy a sense of confidence that your final paper actually makes well-reasoned sense. GRADING: Your papers will be graded according to the following criteria: 1. Is it clearly written, relatively free from careless errors in typing, spelling grammar and syntax? I stop reading papers that are syntactical train wrecks and do not grade them. 2. Is your thesis free from vague and ambiguous language? 3. Is there a logical flow to the structure of the paper? 4. Did you prove your argument valid by formal means? 5. Did you fairly represent the views of those you cite? 6. Did you consider counter arguments to your own? 7. Did you adequately examine the soundness of the premises you use? 8. Did you comprehend what you have been able to demonstrate? 9. Did you hand your paper in on time? 10. Did you do original work? Excellent Internet resources for writing a philosophy paper: APA Style and Format Help with Writing Here are some Valid Syllogisms from successful former student Term Papers. These thesis arguments were successful, not because of 'what' they argued, but rather by 'how' they were argued. AAA-1 BARBARA All individual passion is ruled by individual character. All individual destiny is ruled by individual passion. Therefore,All individual destiny is ruled by individual character. EAE-1 CELARENT No human fetus killing is a private matter. All human abortions are human fetus killings. Therefore, no human abortion is a private matter. (NOTE: by converting the MAJOR premise, this argument could be formulated as a CESARE, EAE-2) AII-1 DARII All perception states are real states. Some dream states are perception states. Therefore, some dreams states are real states. (NOTE: by converting the MINOR premise, this argument could be formulated as a DATISI, AII-3) AII-3 DATISI All things in life that don’t kill you are things that can make your character stronger. Some things in life that don’t kill you are “bad choices” you make. Therefore some “bad choices” you make are things that can make your character stronger. (NOTE: by converting the MINOR premise, this argument could be formulated as a DARII, AII-1) EIO-1 FERIO (All EIO Mood arguments are valid regardless of Figure) No inanimate three-dimensional objects are objects that can commit murder. Some things (i.e. guns) are inanimate three-dimensional objects. Therefore, some things (i.e. guns) are not objects that can commit murder. AEE-2 CAMESTRES All state sanctioned marriages are marriages wherein it is at least logically possible for human procreation to happen. No marriages between members of the same gender are marriages wherein it is at least logically possible for procreation to happen. Therefore, no marriages between members of the same gender are state sanctioned marriages. EAE-2 CESARE No ‘entity’ is a thing that exists outside of sense perception. All ‘god’ things are entities that exist outside of sense perception. Therefore no ‘god’ thing is an ‘entity.’ (NOTE: by converting the MAJOR premise, this argument could be formulated as a CELERANT, EAE-1) AOO-2 BAROKO All 'gay' people are people that politicize their homosexuality. Some homosexual people are not people that politicize their homosexuality. Therefore, some homosexual people are not 'gay' people. OAO-3 BOKARDO Some people that rely on ‘feelings’ in place of ‘reason’ are not ‘critical thinkers and writers’. All people that rely on ‘feelings; in place of ‘reason’ are political ‘liberals.’ Some political ‘liberals’ are not ‘critical thinkers and writers.’ EIO-2 FESTINO No drugs are “recreational”. Some ‘high risk’ sports are “recreational.” Therefore, some “high risk” sports are not drugs. (NOTE: by converting either the MAJOR or MINOR premise this argument could be formulated as a FERISON- EIO-3 or a FRESISON, EIO-4) Many students have asked for a sample term paper that satisfies the necessary and sufficient conditions for formulating a successful term paper in this course. Here is just such an example as your guide. Click the link to access the PDF, Sample Term Paper by Matthew Bixby class of 2007 Yet More resources on Writing a Philosophy Paper Professor Douglas Portmore, Arizona State University has an excellent PDF that both parrallels these guidlines and provides an excellent bibliogrphy for successful writing of undergraduate philosophy papers. Here's the URL for his PDF http://www.public.asu.edu/~dportmor/tips.pdf ---Cordially Professor Mark McIntire 2 3 Copyright © 2013 REASON ARGUE REFUTE: Critical Thinking About Anything by Mark McIntire ISBN: 978-0-615-80070-7 ALL RIGHTS RESERVED: No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopies, recordings, internet, multimedia, television, virtual reality, or by any information storage and retrieval system, without permission in writing from Mark McIntire. MAY BE SOLD BY AUTHORIZED DISTRIBUTORS ONLY First Printing 2007 Thank you for protecting the digital property rights of the author. 4 Table of Contents Copyright Author: Mark McIntire Dedication and Acknowledgments: Part One: Reason Section 1 Basic Logic Concepts Section 2 Twenty Basic Reasoning Distinctions Section 3 Reasoning Fallacies in Three Categories: Irrelevance, Presumption and Ambiguity Section 4 Fallacies of Irrelevance Category Section 5 Fallacies of Presumption Category Section 6 Fallacies of Ambiguity Category Section 7 Part One Reasoning: Learning Review 5 Section 8 Attributes of Critical Thinkers and Writers Part Two: Argue Section 2 Categorical Logic Section 3 Categorical Propositions Section 4 Categorical Syllogisms Section 5 Venn Diagrams & 15 Valid Forms Section 6 The Six Rules of Validity Section 7 Problems with Ordinary Language Section 8 Propositional Logic Overview Section 9 Argument Learning Review Part Three: Refutation Section 1 Section 2 Refute the Definitions Section 23 Refute the Logic Section 4 Refute the Weak Evidence Section 5 Refute by Analogy Section 6 Refute Ethical Or Moral Assumptions Section 7 Part Three: Refutation Learning Review Appendix I: Guidelines for Argumentative Writing Appendix II: Writing a Journal of Your Ideas Bibliography Bibliography Appendix III The 19 Rules of Natural Inference 6 7 Author: Mark McIntire Born in Salem, Massachusetts, Professor McIntire received his undergraduate and graduate philosophy degrees from Oblate College at The Catholic University of America in Washington, D.C. In 1977 he wrote an original one-man-show, “JFK: A Time Remembered” giving over 500 live performances at colleges and universities across America. Author of “The Financial Core Handbook”, Professor Mark McIntire has taught Philosophy since 1966 at Westfield State College, Massachusetts (now Westfield State University), University of Phoenix, Antioch University, and currently teaches online at Santa Barbara City College in California. McIntire was elected to the National Screen Actors Guild Board of Directors in 1983, when he wrote and filed a brief, amicus curiae, with the Supreme Court of the United States in the landmark case CWA v Beck (1986). The high court decision 5-3 sustained McIntire’s argument protecting the freedom of dissident union workers and led to the publication of his work “The Financial Core Handbook” that remains the definitive source on this decision to date. When not teaching Critical Thinking and Writing at Santa Barbara City College online, McIntire conducts executive seminars in “Critical Thinking for Success” and mentors gifted students into their graduate degree programs. In 2010, “The Mark McIntire Show: “MINDS THAT MATTER” ran for 52 episodes on AM 1290 Santa Barbara News Press Radio. The highly rated program featured the life of ideas from college presidents, writers, actors, and scientists and gifted students Supplemental materials for this e-textbook, Reason Argue Refute: Critical Thinking About Anything, are available on Mark McIntire’s online teaching website: http://markmcintire.com 8 9 Dedication and Acknowledgments: It seems fitting for an author of an Aristotelian categorical logic book to acknowledge his indebtedness to others by logical category. In Memoriam: Dr. Peter A. Angeles, Joan McIntire, Ron Pagel, Vernon Olson, Richard Roberts Inspiration: Many thousands of students I have taught since 1966 Nurturing: David L. Hutchinson, Ellen White, Tyler and Whitney Duncan Guidance: Charlton and Lydia Heston, Fraser C. Heston, Christopher Mitchum, Carol Lanning Wisdom: Matthew Kane Bixby, Professor Joseph White, Professor Jim Chesher, Professor Peter Georgakis, Preparation: Mychilo S. Cline, Patricia L. Raabe, Norman P. Stevens, Max Holihan Insistence: Christopher Candy, Gary Gentilini, Michael Miller, Mikal C. Davies, Alastair Patterson Patiently, you have coaxed this book from me. -Cordially, Mark McIntire “Nemo dat...quod non habat." 10 Preface and Introduction “Is not the great defect of our education today--a defect traceable through all the disquieting symptoms of trouble that I have mentioned-that although we often succeed in teaching our pupils "subjects," we fail lamentably on the whole in teaching them how to think: they learn everything, except the art of learning.” ---‘The Lost Tools of Learning’ by Dorothy Sayers, Oxford University, 1947 Welcome to a critical thinking boot-camp for the mind. This is a “how to think” e-textbook for digital devices. Any intelligent person over the age of twelve years old can master basic reasoning, argumentation, and refutation by using this book. Primarily intended for high school college and university students, it can also serve the needs of career professionals in their writing and decision making. Tim McGrath, author of, John Barry: An American Hero in the Age of Sail wrote a gracious testimonial after using this book; “In no small thanks to Reason, Argue, Refute, I wangled a nice advance for a book on the Continental Navy (the Reason section was obviously a bigger help in this instance than the other two – but man, have they been good to learn for the business hours of the day).” This book presents the basics on ‘how to think’ clearly, rationally and logically. The guiding compass of the entire text is the concern for the quality of “how” students think, not with the quantity or content of ‘what’ they think. It is divided into three main parts, each with relevant subsections. Part One: Reasoning gives rigorous training in basic logical ideas, laws, methods and principles as well as an exposition of common fallacies in everyday failed attempts at reasoning. Part Two: Argument gives systematic training in recognizing arguments by type distinguishing arguments by the strength of the inference in their conclusions, analyzing arguments in ordinary language and everyday speech, formulating arguments using both categorical and propositional logic, proving the validity of arguments by formal rules and graphic illustration, and distinguishing between valid and sound arguments. Part Three: Refutation gives effective strategies for refuting arguments by objecting to definitions, weak inductive evidence, causal claims, analogies, and ethical and moral first principles. Ways to look inside (X11 ray or autopsy) arguments for their internal defects are demonstrated leading to cogent refutation by formulating contrary, contradictory and analogical counter arguments. Appendix I offers argumentative writing guidelines that have proven successful for thousands of students. Appendix II offers a reliable format for anyone wishing to write and keep a journal of their “life of ideas.” Throughout this book provocative examples are used sparingly and only to illustrate ideas and methods of effective reasoning, argument, and refutation. This book helps fill a vacuum created by current education curricula. Those curricula advocate teaching “what” to think while giving only flimsy clues as on “how” to think. Current higher education expectations place a premium on “diversity” of opinions while requiring little if any formal training in how to determine valid and sound arguments for or against these diverse opinions. Why Read This Book? Now, at the beginning of the twenty-first century it is common for students to receive a Bachelor’s, Master’s, and even a Doctoral degree from higher education institutions without ever being formally trained in reasoning, argumentation, and refutation. This fact adequately explains the disappointing failure of higher education globally to reliably educate individuals who know “how” to think. The growing demand for “Critical Thinking for Success” training seminars for business managers gives even more evidence of the neglect of critical thinking in schools, colleges and universities. Even worse, in many instances what passes as training in critical thinking, even at university level, is little more than asking students, “Well...how do you feel about that?” Why do students need to learn “how” to think formally? To answer this question we need to recall that higher education policy in the late 1960’s shredded the “core curriculum” for a variety of well intentioned but ultimately calamitous reasons. Prior to the early 1970s no college student could earn a degree in the arts and sciences without required formal training in the processes of reasoning and argumentation in the core-curriculum. This formal training was usually, but not exclusively, conducted by the philosophy department faculties. Some Math courses and some English courses also fulfilled this requirement, and still do to 12 this day. The point is that, prior to the early 1970s, the requirement for formal training in formal reasoning was fundamental to the very notion of a liberal arts education of receiving a Liberal Arts education. All that changed as “cultural relativism” and “social diversity” gradually became the expected outcomes in much of the American higher education curricula into the mid 1970’s and beyond. By the time the graduates of this “outcome based” curricula became teaching faculty themselves through the 80’s, 90’s, and on into the new millennium, little trace of a common logic could be found throughout many academic curricula. Standards for testable proof also eroded with the rising tide of “cultural relativism.” In some curricula, the systematic denial of reason based on logic and best evidence became common while the academic disciplines fragmented. Settling academic debates became more a matter of advocating a preconceived notion of ‘social justice’ rather than conducting critical thought. Everyone’s opinion was (and in some cases still is today) viewed as equally valid and sound regardless of its logical absurdity or lack of testable evidence. While this erosion of academic standards progressed, many astute intellects objected strenuously to a lowering of academic reasoning standards. The citation above by Dorothy Sayers is only one example and that was delivered over forty-five years ago. “From the twelfth century through the early twentieth century,” wrote Margaret Ferguson of Yale University in 1977, “the curriculum of the western university put great emphasis on the arts of argumentation—the arts of Aristotle called dialectic and rhetoric and distinguished from all other branches of human knowledge on the basis of their capacity to draw opposite conclusions impartially. Teachers and students, people at every level of the university’s hierarchy, were continually practicing and developing argumentative skills…the university provided a forum in which critical thinking (within certain limits) was not only allowed but encouraged…The problem we face today…is that the enabling conditions of debate are atrophying both within the university and in its relations to society…What I propose is that the university should spend time and some of its dwindling money on devising ways to preserve genuine debate” [Yale Magazine and Journal, November 1977, p.11.] Her admonition was swept aside while academic curricula were reshaped according to the new canons of ‘social justice’ and ‘social outcomes’. The underlying assumption of this book is the notion that rational thinking is 13 a cultivated art that applies the discipline of logic and search for best available evidence to any debatable topic in any academic discipline. Neither of these alone is sufficient for cultivating the art of critical thinking. Both are, however, necessary conditions for the life long process of a rational thinker seeking truth and wisdom. Reasoning beyond our feelings is the sub textual premise for this book. However, it would be a gross miscalculation to infer from this that the author underestimates the role of our emotions in the seeking of happiness in wisdom. On the contrary, no rational person could exit the bed in the morning without the stir of passion to think, act, and change the world into a better place. Finding truth through reason, however, entails a marriage of emotion tempered by intellect. Otherwise we would do better to stay in our beds. Why is this book superior to other books already available? Unlike most critical thinking books now flooding the market, this text does not seek to entertain, or to incite with ideological bias. Rather, it provides grounding in the basics of artful reasoning that has stood the test of time and application. This book is a bare bones, no nonsense instruction in how to seek truth through logic and best evidence. Reason Argue Refute: Critical Thinking About Anything includes a unique feature not found in any other book currently available to serious students of reasoning and argumentation. Almost one-third is devoted to mastering the ultimate power of any well trained mind, the power of refutation. This book provides sound strategies not only for refuting the arguments of others, but more significantly, for testing the arguments we formulate ourselves. Reason Argue Refute: Critical Thinking About Anything was suggested by Professor Gary Gentilini of the University of Phoenix. Thank you, Gary. Introduction. Contrary to what some educators may claim, there are ‘good’ arguments and there are ‘bad’ arguments and we can tell the difference. When we use logic backed by best evidence we make good arguments. If our logic is defective and/or if our evidence is weak, then we make bad arguments. Critical thinking entails knowing the difference between the two, and then applying good arguments and refutations to debatable topics among reasonable people. This book will teach you how to think, not what to think. The good news is that we are all born with the ability to think. Unfortunately, only a 14 few of us are ever trained how to think clearly, precisely, and consistently regardless of the subject matter on a consistent basis. That’s what this book will do for you; give your thinking a reliable structure to ensure good reasoning for the rest of your life of ideas. This will be done by sorting out failed attempts at reasoning called informal fallacies from successful acts of reasoning called sound argumentation. We use logic to sort things out. We use best available evidence to separate good, better, and best arguments from weak, defective and worst arguments. This book will teach or improve your ability to use both in serious debate and discourse. If you want to apply good reasoning to your written es says and term papers, then study Appendix I. Have you ever wanted to keep a personal journal of your ideas? If so, then implement the format for writing your journal of ideas in Appendix II. We begin our study of critical thinking and writing by understanding the process of reasoning. Here, we begin our mastery of the critical thinking and writing arts and methods by stipulating: Twenty Distinctions for Critical Thinkers. If you get nothing more from this book other than these reliable mental distinctions they will bring clarity to your perception, coherence to your ideas and effective tools to dissect ideas and arguments from opinions. They form the conceptual core of this work. Here they are. Later, they will be presented again with examples: Twenty Distinctions for Critical Thinking Beliefs / Knowledge: Beliefs are opinions we accept as true or • false. Knowledge is accepting beliefs when confirmed by logic and best evidence. Sentence / Proposition: Any syntactically and grammatically • correct group of words is a sentence, whereas only those sentences that state a claim is either true or false are propositions. Syntax / Grammar: The general rules for ordering words in a • language is syntax, whereas the specific set of rules for proper usage of words in a language is grammar. Assumption / Presumption: Any claim accepted as true in • reasoning to another claim is an assumption, whereas a presumption is using an assumption in the process of reasoning. Connotation/Denotation: In logic, the unique qualities or • attributes common to all referred to by a term is its connotation, whereas a list 15 of only those individual things having those unique qualities or attributes constitutes a term’s denotation. (Note: Other academic disciplines ascribe broader associative meaning to “connotation.”) Subjectiveclaim/Objective claim:Any truth claim that cannot be • independently verified as true or false is a subjective claim, whereas any truth claim that can be independently verified as true or false is an objective claim. Imply / Infer: To leave conclusions that may be drawn by • others is to imply. To draw conclusions from what is implied is to infer. Explanation / Argument: Explanations provide information • about who, what, how, when, where, and even why a statement is either true or false; whereas arguments provide reasons for accepting that the statement is either true or false. Premise / Conclusion: A premise is a • Proposition offered as a reason for accepting the truth or falsity of another proposition called a conclusion. Formal / Informal Argument: A formal argument is any argument that has all stated premises a n d a stated conclusion according to an established pattern of inference. An informal argument may have missing premises that are thought to be reasonable assumptions in a pattern of reasoning. Logic / Rhetoric: Logic is the study of making inferences in the • process of reasoning. By contrast, Rhetoric is the art of evoking desired responses by any linguistic means available. Logical possibility / Empirical Probability: Any claim that does • not contradict itself is a logically possible claim. However, only logically possible claims that can, in fact, be verified by observable, test able evidence, are empirically probable claims. Fallacy / Error: Fallacies, whether formal or informal, are • conclusions arrived at by some mistake in the process or pattern of reasoning itself. Errors are merely cognitive miscalculations or misperceptions. Valid / Sound: A deductive argument is valid if the conclusion • follows from the premises by necessity, i.e., on the assumption that the premises are true, then the conclusion would also have to be true. A deductive argument is sound if, and only if a) it is valid, and b) the premises of the argument are true according to best available evidence either 16 analytically or empirically. Deductive / Inductive: When it is claimed that a necessary • conclusion is drawn out of premises given as reasons to accept it, then that phase of the reasoning process is called deductive. When a “probable” or “likely” conclusion is projected from verification of instances cited, then that phase of the reasoning process is called inductive. Inductive probability can range anywhere from “weak” to “strong. Necessary Conditions / Sufficient Conditions: Any elements • required for events to take place are known as necessary conditions. Any elements that are enough for something to take place are known as the sufficient conditions. Causes/Effects: Those necessary and sufficient conditions • thought to be required in order for another event to take place are called causes. Any events that result from those necessary and sufficient conditions actually taking place are called effects. Analytic / Synthetic: Propositions derived from a purely mental • examination of ideas and their elements are analytic. Propositions determined as true or false from observations or facts are synthetic. a priori / a posteriori: Knowledge independent of observation is a • priori knowledge (Latin: a priori, before the fact). Knowledge after observation is a posteriori knowledge (Latin: a posteriori, after the fact). Ethical Principles / Moral Codes: Any set of general rules or • laws thought to govern human conduct constitutes ethical principles. Any set of maxims, guides, or precepts that apply ethical principles to particular human conduct constitutes moral codes. 17 Part One: Reason 18 Section 1 Basic Logic Concepts Working Definitions of Basic Logic Concepts: Truth: Any claim to fact that is analytically or empirically verified to coherently and consistently correspond to both the rules of precise definitions, and formal logic backed by best available evidence; that cannot be falsified. Proposition: Any sentence that claims something is true or false either analytically or empirically. Argument: Any set of propositions (premises) that provide reasons to infer the truth or falsity of another proposition (a conclusion) either deductively or inductively. Inference: Any mental process that draws a conclusion truth claim from premise truth claims. Premise: Any proposition that is used as a reason to infer the acceptance of another proposition Conclusion: Any proposition that is inferred from a set of premises. Deduction: Any inference processes that ‘draws out’ one proposition (conclusion) from other propositions (premise or premises) by necessity. (Latin: deduco, to lead out of or from) Induction: Any inference processes ‘leading up to or away from’, a probable conclusion that seems likely based on sufficient individual instances being enumerated. (Latin: induco, to lead up to.) Explanation: Any set of statements that answer the, who, what, when, where, how, or even why questions of any physical or mental event. Valid Argument: Any deductive reasoning process that entails a conclusion from stated premises by logical necessity such that if the premises are true then the inferred conclusion must be true as well. Invalid Argument: Any deductive reasoning process that fails to entail its conclusion from its states premises by logical necessity. Soundness: When any valid deductive argument is composed of all 19 analytically or factually true premises. Cogency: Any line of reasoning that is clear, logical sound and convincingly backed by testable evidence. Rhetoric: Any use of language or image purely calculated to persuade regardless of factual truth or logical validity. Logic: Formal study of ideas, laws, rules, or methods that ensure conclusions follow from premises either by deductive necessity called ‘entailment’, or by inductive probability. Categorical Logic: First codified by Aristotle (and hence sometimes called Aristotelian logic), refers to the rules for necessary inferences about members of one class being included as members, or excluded as members of another class, set, group or category. Propositional Logic: A system of symbols (and hence sometimes called symbolic logic) standing for whole or partial propositions, related by logical operators (‘and’, ‘or’, ‘if...then’ etc.) that connect whole or partial propositions resulting in necessary inferences construed as the ‘Rules of Natural Inference’. Note: These are working definitions only. They are not offered as final, precise definitions that resolve all legitimate philosophical debate. Other academic disciplines have different, more specific definitions that are proper for their field of study. Beginning students of critical thinking and writing can use these definitions to stimulate larger philosophical debate as they move through this text. 20 Section 2 Twenty Basic Reasoning Distinctions Good distinctions are the sharp knives of reasoning. To better understand our basic definitions used in the process of reasoning, it is essential to make a list of useful, basic linguistic distinctions. When we make good distinctions between ideas we understand how they differ from each other. If we understand how two ideas differ from each other, then we understand more clearly what those ideas really mean. Conversely, when we fail to make necessary distinctions in the meaning of ideas we run the risk of falsely supposing that there is little or no difference between ideas that are, upon reflection, quite different. Good reasoning requires that words have definite and discernible meanings through distinctions. The following list of basic distinctions, once mastered, provides students with invaluable ‘cutting tools’ that reveal what ideas really mean, and, sometimes more significantly, what ideas do not mean. As you read them, think of them as a dialogue of differences. Try to formulate examples that illustrate these distinctions in your notebook. Use these distinctions to keep a journal of your ‘life of ideas’. If you learn nothing more than these twenty distinctions, your investment in this book will pay dividends in better reasoning skills for life. Students who master these distinctions report greater ‘clarity’ and ‘precision’ in reasoning. Whereas they formerly used these terms interchangeably, now they choose their words more carefully with gratifying results in the quality of their reasoning. Good reasoning begins with precisely distinguishing differences between ideas in any debate. Here, then, is the list of twenty essential distinctions for critical thinking in the reasoning process. Beliefs / Knowledge: Beliefs are opinions we accept as true or false. Knowledge is accepting beliefs when confirmed by logic and best evidence. Examples: “In my opinion, all swans are white.” (Belief). “With the discovery of black swans in Australia, I now know that not all swans are white. Some swans are black.” (Knowledge) Sentence / Proposition: Any syntactically and grammatically correct group 21 of words is a sentence, whereas only those sentences that propose that a given claim is either true of false are propositions. Example: “Close that door!” is a proper sentence, but it is not a proposition. “All Popes are Catholics.” is a proposition (truth claim) as well as a proper sentence. Not all sentences are propositions, but all propositions are sentences. Syntax / Grammar: The general rules for ordering words in a language is syntax, whereas the specific set of rules for proper usage of words in a language is grammar. Example: “Up with put, I will not you.” This sentence violates the rules of syntax in the English language. “There’s keys on the table.” is a sentence that violates the rules of grammar in the English language. Assumption / Presumption:Any claim accepted as true in reasoning to another claim is an assumption, whereas a presumption is using an assumption in reasoning. Example: “Based on the assumption that you want to earn your own keep around here, I presume you are looking for gainful employment.” Connotation / Denotation: In logic, the unique qualities or attributes common to all referred to by a term is its connotation, whereas a list of only those individual things having those unique qualities or at tributes constitutes a term’s denotation. (Note: Other linguistic studies ascribe broader associative meaning to connotation.) Example: Article 1, Section 3 of the United States Constitution enumerates the exclusive attributes and requirements necessary for the connotation of the term ‘United States Senator’. A complete list of all those who ever did have, or do now have these exclusive at tributes, and fulfilled these requirements is the denotation of the term ‘United States Senator’. Subjective claim/Objective claim: Any truth claim that cannot be independently verified as true or false is a subjective claim, whereas any 22 truth claim that can be independently verified as true or false is an objective claim. 23 Example: “My daily horoscope is true for me.”(Subjective claim) “A fire will not occur without fuel, oxygen, and a source of combustion.” (Objective claim) Imply / Infer: To leave conclusions that may be drawn by others is to imply. To draw conclusions from what is implied is to infer. Example: “She inferred what you implied.” Explanation / Argument: Explanations provide information about who, what, how, when, where, and even why a statement is either true or false; whereas arguments provide reasons for accepting that the statement is either true or false. Example: Planets are celestial bodies in a solar system that dominate their orbit around a central sun. (Explanation about what a ‘planet’ is.) Celestial bodies whose orbit is not disturbed by other celestial bodies are ‘planets’. Pluto’s orbit is disturbed by other planets. Therefore, Pluto is not a ‘planet’. (Argument against Pluto being a planet) Premise / Conclusion: A premise is a proposition offered as a reason for accepting the truth or falsity of another proposition called a conclusion. Example: “If I want to stay healthy, then I should stop smoking cigarettes (premise). I want to stay healthy (premise). Therefore, I should stop smoking cigarettes (conclusion). Formal / Informal Argument: A formal argument is any argument that has all stated premises and a stated conclusion according to an established pattern of inference. An informal argument may have missing premises that are thought to be reasonable assumptions in a pattern of reasoning. Example: “Monkeys climb trees. I am a monkey. Therefore, I climb trees.” (Formal argument) “No, I don’t climb trees; I’m no monkey.” (Informal argument) 24 Logic / Rhetoric: Logic is the study of making inferences in the process of reasoning. By contrast, Rhetoric, in its primary meaning, is the art of evoking desired responses by language, speech or image. Example: If you bought this book because you thought that the contents might help you in your study of critical thinking, then you inferred reasonably by logic. If you bought this book solely because your mother told you to, then you were persuaded by bad rhetoric. Logical possibility / Empirical Probability: Any claim that does not contradict itself is a logically possible claim. However, only logically possible claims that can, in fact, be verified by observable, testable evidence, are empirically probable claims. Example: Given certain assumptions, ‘time-travel’ is certainly logically possible, but it is not yet empirically probable. Fallacy / Error: Fallacies, whether formal or informal, are conclusions arrived at by some mistake in the process or pattern of reasoning itself. Errors are merely cognitive miscalculations or misperceptions. Example: “No one’s ever disproved astrology, so therefore the claims of astrologists must be True”. (Fallacy from ignorance) “Anyone born in April is a ‘Leo’. (Astrology error) Valid / Sound: A deductive argument is valid if the conclusion follows from the premises by necessity, i.e., on the assumption that the premises are true, then the conclusion would also have to be true. A deductive argument is sound if, and only if a) it is valid, and b) the premises of the argument are true according to best available evidence either analytically or empirically. Example:All light bulbs are human. All Bostonians are light bulbs. Therefore, all Bostonians are human. (Valid but not sound.) No light bulbs are human. All Bostonians are human. 25 Therefore, no Bostonians are light bulbs. (Valid and sound) Deductive / Inductive: When it is claimed that a necessary conclusion is drawn out of premises given as reasons to accept it, then that phase of the reasoning process is called deductive. When a ‘probable’ or ‘likely’ conclusion is projected from confirmation of instances cited, then that phase of the reasoning process is called inductive. Inductive probability can range anywhere from ‘weak’ to ‘strong’, but never absolutely certain. Examples: “All classes currently taught at City Colleges are taught by highly qualified professors. Critical Thinking and Writing is a course currently taught at City College; therefore, Critical Thinking and Writing currently taught at City College is taught by highly qualified professors.” (Deductive argument) “My brother took classes at City College last semester and all were taught by highly qualified professors. My sister took classes at City College last semester and she reports the same thing. In all probability, the classes I take at City College next year will be taught by highly qualified professors as well.” (Inductive argument) Necessary Conditions / Sufficient Conditions: Any elements required for events to take place are known as necessary conditions. Any elements that are enough for something to take place are known as the sufficient conditions. Example: The precise moment of ignition, by any means, is the sufficient condition for the necessary conditions of fuel, oxygen, and source of ignition to actually take place in a fire. Causes/Effects: Those necessary and sufficient conditions thought to be required in order for another event to take place are called causes. Any events that result from those necessary and sufficient conditions actually taking place are called effects. Example: Sparks from a welder’s torch on the roof of the building 26 showered down on a stack of gasoline soaked newspapers several floors below (causes). As a result the building caught fire and was destroyed (Effects). Analytic / Synthetic: Propositions derived from a purely mental examination of ideas and their elements are analytic. Propositions determined as true or false from observations or facts are synthetic. 27 Example: (analytic proposition) “If he’s a bachelor, then he’s not married.” (Synthetic proposition) “The City of Chico, California is approximately 476.4 miles from the city of Santa Barbara.” a priori / a posteriori: Knowledge independent of observation is a priori knowledge (Latin: a priori, before the fact). Knowledge after observation is a posteriori knowledge (Latin: a posteriori, after the fact). Example: (a priori) “Squares are four sided figures.” (a posteriori) “This square is half the size of that square.” Ethical Principles / Moral Codes: Any set of General rules or laws thought to govern human conduct constitute ethical principles. Any set of maxims, guides, or precepts that apply ethical principles to particular human conduct constitutes moral codes. Example: (ethical principle) “Treating others as we would wish to be treated is our duty as human beings.” (Moral code) “Do no harm.” (Hippocratic Code) 28 29 Section 3 Reasoning Fallacies in Three Categories: Irrelevance, Presumption and Ambiguity Fallacies are failed attempts at reasoning. Part of knowing what successful reasoning is entails knowing what successful reasoning is not. We now take up the study of informal fallacies in the process of reasoning. Reasoning fallacies are not like errors of fact, they are mistakes in the process of thinking. Like some lost traveler, fallacies happen when the mind takes a wrong turn trying to negotiate an inference. You can make an error in trying to balance your checkbook, but it would be improper to accuse you of committing an informal fallacy. However, you can be accused of committing an informal fallacy if, in the act of reasoning, you are vague, ambiguous, careless, presumptive, or allow some unrelated factors to mistakenly divert your premises from a necessary conclusion. These reasoning mistakes are quite common in every day discourse. We need not strain hard to find news reports, film ‘documentaries,’ TV commercials, internet ‘blogs’, serious discussions, and debates in public and private life replete with informal fallacies of reasoning. We are all human and we all commit these mistakes in reasoning though we are slow to admit it, and quick to point it out in others. Critical thinkers and writers, however, constantly develop the necessary self-discipline to both recognize and eliminate these mistakes in their reasoning process. Note that informal fallacies are often mixed, by clever minds, into ‘cocktails’ of several fallacies all in the same argument. Often it’s a powerful brew concocted by those with full intent to deceive their audience. It is also noteworthy that these informal fallacies are sometimes not only deliberately committed in order to deceive those seeking truth, but also to intentionally coerce some action on the part of the listener or reader. Manipulation of public and private opinion is serious big business in the age of media technology. Worse still, deliberate distortion of fact through informal fallacies is a nonpartisan, nonsectarian, equal opportunity, intellectual sport for some. Today’s political ‘Gotcha-Culture’, the new shortcut to fame, money and power, is as invidious as it is insidious. Critical thinkers need to beware. Example: “If you’re not a progressive thinker, then you must be stupid.’”(You could substitute any political ‘stereotype’ with the same 30 resulting fallacy.) As you read this section on informal fallacies you will find some of them humorous. You will ask yourself, “How can anyone think that way?” Look in the mirror. For easy study purposes and logical arrangement, we divide these reasoning mistakes into three categories, and then we subdivide these into members of those categories. Examples are given but you will do yourself a great service if you keep a record of the informal fallacies you encounter in your daily routine. Put them in your journal of ideas. Read them to your children. They will thank you. There are three main categories of informal fallacies: Informal Fallacies of Relevance: In fallacies of relevance, arguments rely on premises which may seem related to the conclusion, but which in fact are not. Relevance here is understood as being related to the issue under debate. Informal Fallacies of Presumption: Fallacies of presumption contain dubious or false premises in need of factual proof that are simply assumed to be true. Presumption here is understood as being an unquestioned acceptance. Informal Fallacies of Ambiguity: In fallacies of ambiguity, reasoning goes awry because words, phrases, or entire propositions with more than one clear, definite meaning in the argument are misleading and therefore cannot imply the conclusion with logical necessity. Ambiguity here is understood as being confused about exact meaning. Many of these informal fallacies have Latin names that have passed into common usage. Therefore, our discussion includes their Latin etymology in parenthesis; to better enlighten serious students of reasoning. Now we master the most common informal fallacies in each category. First, let’s consider major examples of relevance fallacies 31 Section 4 Fallacies of Irrelevance Category Irrelevancies derail reasoning. Fallacies of Relevance rely on premises that might seem to be related to the conclusion when, in fact, they are not related necessarily or even accidentally. There are seven major fallacies of relevance that we study here. 1. Argument from Ignorance(Latin:ad ignorantiam, from ignorance,): When it is argued that a proposition is true because it has not been proved false, or when it is argued that a proposition is false because it has not been proved true then the ad ignorantiam fallacy is committed. Example: Since no one has disproved the theory of evolution, the theory of evolution must be true. 2. Appeal to Inappropriate Authority (Latin: ad verecundiam, from respect,): When the premises of an argument appeal to the judgment of some party or parties having no legitimate claim to authority in the matter at hand, then the ad verecundiam fallacy is committed. Example: Gloria Diva just returned from Berlin and she says that Germany’s new chancellor, Adolph Hitler, is a compassionate leader of the German people. That’s good enough for me because I love all Gloria’s movies. If Gloria likes Herr Hitler, then he must be a kind leader of the German people. 3. Argument Against the Person(Latin: ad hominem, to the man or person): When an attack is leveled not at the claims being made, or the at the merits of the argument made, but directly at the person making the argument, then it is a fallacy ad hominem. Arguments ad hominem come in two flavors: When the attack is directed against the person making a claim, seeking to defame or discredit them as a person it is called an ‘abusive ad hominem.’ Example: “Don’t believe anything he says. He never takes a shower.” 32 When the attack is indirectly against a person, suggesting that they hold their views chiefly because of their special circumstances, interests or associations, then it is a ‘circumstantial ad hominem’. Example: “I find it interesting that all the Senators who voted for drafting 18 year olds into the military are themselves well beyond draft age.” 4. Appeal to Emotion(Latin:ad populum, to the populace): When careful reasoning is replaced with devices calculated to elicit popular enthusiasm and emotional support for the conclusion advanced, then the ad populum fallacy is committed. Example: So, our President lied about having extramarital sex in the Oval Office of the White House. Cool! Everybody lies about sex. 5. Appeal to Pity(Latin:admisericordiam, from pity): When careful reasoning is replaced by devices calculated to elicit pity from the listener and to distract from the issue in question, then the ad misericordiam fallacy is committed. Example: “You can’t fail me in this course! I NEED this course to transfer to University, and my parents will kill me if I don’t transfer this semester”. 6. Appeal to Force (Latin: ad baculum, to the stick): When careful reasoning is replaced with direct or insinuated threats of force or coercion to bring about the acceptance of some conclusion, then the ad baculum fallacy is committed. Example: “If you want that raise next month, you better endorse my uncle in the next city council election.” 7. Irrelevant Conclusion (Latin: ignoratio elenchi, ignorance of refutation) When the premises miss the point, purporting to support one conclusion while in fact supporting or establishing another, then 33 the ignoratio elenchi fallacy is committed. Example: “This is ridiculous. Here I am being ticketed and fined for speeding while thugs roam the streets committing violent crimes at will. The police should leave me alone and hunt down those dangerous criminals.” It may be the case that the police need to hunt down violent criminals. However, that is unrelated to deserving a ticket. 34 Section 5 Fallacies of Presumption Category Buried assumptions are land mines in reasoning. The presumption category of mistaken (fallacious) arguments arises from reliance on propositions that are assumed to be true, but are in fact false, dubious or without warrant by sufficient evidence. Here we explain the types of reasoning mistakes in five fallacies of presumption: 1. Complex Question: When a question is asked in such a way as to presuppose the truth of some assumption or question buried in the original question, then the Complex Question fallacy is committed. The answer to one question cannot be presumed in order to give evidence for another question. The questions need to be ‘divided’ and each considered on its own merits. Example: “What color paint are you drinking today that makes you say something that absurd?” 2. False Cause (Latin: post hoc, ergo propter hoc, after this, therefore because of this): When one mistakes as a ‘cause’ some factor that is really only a temporal sequence, correlation or association, then the False Cause fallacy is committed. (Causal arguments are often difficult to prove conclusively, as will be seen in Part Three: Refutation.) Example: “My dad, cheated on his taxes last year, and his business went belly-up this year. That’s how Karma works dude.” 3. Begging-the-Question: (Latin: petitio principii, seeing the premise): When one assumes in the premises of an argument the very truth of what one seeks to establish in the conclusion of that argument, then the petitio principii fallacy is committed. Example: “The reason I’m so popular is that everybody likes me.” (Reputed quote from Muhammad Ali). 4. Accident: When one applies a generalization of a principle or general rule to an unusual individual case that it does not properly govern, then the fallacy of Accident is committed. Example: Anyone swimming in the city reservoir will be prosecuted and fined. The police should therefore arrest and prosecute the paramedic that 35 rescued a drowning child who fell into the reservoir. 5. Converse Accident: This is just the reverse of Accident. When one moves carelessly or too quickly from an unusual single case to an indefensibly broad generalization, rule or principle, then the fallacy of Converse Accident is committed. Example: Oprah Winfrey is a woman, and she is paid more money than any male talk-show host. Therefore, female talk-show hosts, as a rule, are paid more money than male talk-show hosts. 36 Section 6 Fallacies of Ambiguity Category Mental misdirection is the basis of humor. When the mind is misdirected by ambiguous words, phrases, signs, accents, even entire sentences there’s usually a punch line soon to follow. When ambiguity infects reasoning then erroneous conclusions usually result. Nothing can be inferred with certainty from ambiguity because ambiguity means confusion of at least two meanings. In these mistaken, but often funny, arguments reliance is on some shift in the meaning of words, phrases, or even entire sentences, from their meaning in the premises to some other meaning in the conclusion. Professional comedians are keen practitioners of ambiguity fallacies. The essence of humor relies on misperception. It is precisely this misperception that enables ambiguity to lead us in mental misdirection often with humorous but sometimes foolish mistakes in reasoning, 1. Equivocation: When the same word or phrase is used with two or more meanings, deliberately or accidentally, in the formulation of an argument, then the fallacy of Equivocation is committed. Example: Rare books are expensive. Great novels are rare books. Therefore, great novels are expensive. 2. Amphiboly: When one of the statements in an argument has more than one plausible meaning, due to the loose or awkward way in which the words in that statement have been combined, then the fallacy of Amphiboly is committed. Example: "Customers are required to remove all their clothes when dryer stops.” (Amphibious sign in a Laundromat). 3. Accent: When a shift of meaning arises within an argument as a consequence of changes in the vocal stress or graphic emphasis given to its words, then the fallacy of Accent is committed. Example:“My name is Schvink, and whadi-ya-think, I’ll press your pants for nothing.” (When read with vocal accent of a declarative sentence, it 37 means that you get free pressing of your pants. However, when read with the vocal accent of a question, it means; do you really think I’ll press your pants for free? Are you insane? 4. Composition: This fallacy is committed: a) when one reasons mistakenly from the attributes of a part to the attributes of the whole, or b) when one reasons mistakenly from the attributes of an individual member of some collection to the attributes of the totality of that collection. The fallacy of Composition, and its sister fallacy of Division are often referred to as ‘Part-To-Whole’ fallacies. Here’s why. Example: I’m thinking of buying a new Macintosh e-book computer and I found out that the onboard speakers are really inexpensive. Therefore the laptop itself must be really inexpensive. 5. Division: Conversely, the fallacy of Division is committed a) when one reasons mistakenly from the attributes of a whole to the attributes of one of its parts, or b) when one reasons mistakenly from the attributes of a totality of some collection of entities to the attributes of the individual entities within that collection. Example: Smith College is a very wealthy college. I’m dating a girl from Smith, so she must be very wealthy. These17informalfallaciesdonotexhaustthelistof recorded fallacy types. They are simply the most common. Other texts use subtle variations of these with different names. Some examples you will find include: ‘Red Herring’ is kind of irrelevance fallacy that tries to throw the listener off track by mentioning an unrelated point “Straw-Man” deliberately misrepresents another’s views in order to more easily refute them. “Slippery-Slope” can be a variation of an unsupported or improbable “false cause” fallacy. 38 “Hasty Generalization” can be either Accident/ Converse Accident irrelevancy or Division/ Composition ambiguity in some texts (see example above). “Non-sequitur” (Latin: it does not follow) is a popular general expression for ignoratio elenchi(see example above). “Euphemisms” substitute “pleasant” language to refer to something “‘unpleasant”. “Dysphemisms” substitute unpleasant language to refer to something that is pleasant. Example: He’s not stupid, mom. He’s just ‘special’. “Tu Quoque” is another variation of the ad hominem fallacy. Tu quoque (Latin: you too) is the fallacious attack on a person because they may be guilty of the very thing they accuse others of doing or saying. Example: You’re a fine one to preach to me on the evils of my drug addiction when you got hammered every night yourself when you were my age. 39 Section 7 40 Part One Reasoning: Learning Review Ok, what have you learned? All of these informal fallacies echo off the walls of your daily conversations, observations, and your very own thinking. Now you can appreciate the true significance of the title of this book. Reviewing informal fallacies makes us realize just how easy it is to be fooled by simple mistakes in the process of reasoning. Good reasoning is the exception and not the rule in ordinary life, even your own. Now that you’re determined to be a critical thinker let’s review where you are. Reasoning or “critical thinking” is the mental discipline of identifying, analyzing, evaluating, constructing, and refuting both informal and formal written and oral arguments based on documented, verifiable proof regardless of topic. Reasoning is, therefore, the process of arriving at valid deductive arguments and/or cogent inductive arguments in spoken or written debate. Reasoning proficiency results in the conceptual agility to employ the science of logic in the rigorous search for ‘best evidence’. Such proficiency requires a creative and imaginative acuity, a blend of art and science. It shows its highest fulfillment in the art of refutation. Achieving this level of valid and cogent reasoning, then, requires a review of what we have learned so far about the process of reasoning. A “learning review” will conclude each part of this book. Serious students of reasoning will use these learning reviews as a checklist in their notebooks or journal. In going over this checklist students can determine for themselves if they have sufficient knowledge of the ideas and definitions in Part One: Reasoning to advance to the next, Part Two: Argument. This is an ideal way to check your progress, for if you can do all these things one step at a time, then you are well on your way to proficiency in critical thinking. If you cannot do all these things, then you need to review Part One until you can. Use the Twenty Reasoning Distinctions in Part One, Section 2, to sharpen your skills in reaching these objectives. After studying Part One: Reasoning, you should be able to: •Recognize authentic debatable topics for informal and formal argumentation in oral or written format. •Understand the difference between Rhetoric and Logic in oral and written format. •Understand the difference between a sentence and a proposition. 41 •Recognize informal deductive and inductive arguments oral or written format. •Understand the difference between knowledge and belief. •Distinguish between validity and soundness as different attributes of arguments. •Identify premises and conclusions in informal arguments in both oral and written format. •Recognize informal fallacies in everyday debate and discourse in oral or written format. •Understand the difference between fallacies of irrelevance, presumption, and ambiguity. •Understand the different roles played by explanations and arguments in the process of reasoning. •Develop a sense for recognizing assumptions and/or presumptions in reasoning. •Avoid committing informal fallacies in the process of reasoning on debatable topics in any academic discipline. 42 Section 8 Attributes of Critical Thinkers and Writers Accomplishing these objectives develops desirable as well as useful attributes of the intellect. This is a good place to review a list of those attributes found in a proficient reasoning mind of a critical thinker and writer. Such a person is one who: Relies on reasons instead of emotions in deciding answers to debatable questions. • Distinguishes truth claim statements that are matters of belief from those that are matters of knowledge. • Accepts the limitations of their own general background knowledge about debatable questions. • Separates provable truth from myth, superstition, cultural influence, and personal prejudice. • Understands that provable truth is a separate issue from logical validity in deciding debatable questions. • Establishes a clear set of analytical criteria for accepting truth claims and arguments on debatable questions. • Consciously recognizes their own beliefs, assumptions, presumptions, myths, superstitions, and opinions and weighs them against provable facts. Carefully and considerately examines the views of others on debatable questions. • Accepts that critical thinking is a perpetual state of self-assessment and self discipline on debatable questions. • Withholds judgment until all testable facts and reasonable arguments have been considered. • Avoids fallacies, invalid arguments, and unverifiable evidence in examining truth claims, assumptions, and beliefs. • Modifies their own opinions in the light of new facts and more reasonable arguments. • Formulates only valid deductive arguments in speaking and writing. • Formulates cogent inductive arguments to test for provable facts. • Formulates counter-arguments and refutations to weak arguments. • Formulates spoken and written arguments free of ambiguity, presumption, and irrelevance. • Seeks a life of ideas with others. • 43 44 Arguments: Deductive and Inductive Deductive / Inductive: When it is claimed that a necessary conclusion is drawn out of premises given as reasons to accept it, then that phase of the reasoning process is called deductive. When a ‘probable’ or ‘likely’ conclusion is projected from verification of instances cited, then that phase of the reasoning process is called inductive. Inductive probability can range anywhere from ‘weak’ to ‘strong’. Using number 15 of our Twenty Distinctions for Critical Thinkers as a start point we notice a fundamental difference between deductive inferences and inductive inferences in argument. Deductive inferences are arrived at out of logical necessity called ‘entailment’. Inductive inferences on the contrary are arrived at based on some degree of likelihood called ‘probability’. To recognize this is to acquire the mental skill in discerning deductive from inductive arguments. Astonishingly, many well educated people lack this mental skill. Yet a simple focus on this distinction makes the discernment easy. Here’s how. When this inference happens out of logical necessity in a deductive argument, then the premises are said to entail the conclusion and the argument is valid. If the inference fails, for whatever reason, to entail the conclusion by logical necessity, then the deductive argument is invalid. There is no middle ground on this point. A deductive argument is either valid or invalid. Just as no female can be ‘partially’ pregnant, so too, no deductive argument can be ‘partially’ valid. Like the game of horseshoes you don’t get points for ‘almost’. It’s all or nothing when it comes to the validity of deductive arguments. This logical principle is violated in popular speech and writing quite often. We hear, and read aberrations such as, “Her argument is more valid than any of the others,’ or ‘He made a valid point.’ Such usage, however popular, indicates a lack of formal training in reasoning and argument. Such is not the case with inductive arguments. Unlike deductive arguments, inductive arguments rely on a different sort of inference that has nothing to do with necessary entailment. Inductive arguments rely on the theory of probability for their strength. A strong inductive argument relies on a strong probability. To the degree that inductive arguments lack that strength is the degree to which they fall form strong to weak to 45 almost worthless. Serious students of argumentation can save themselves much confusion by only using the terms ‘valid’ and ‘invalid’ when referring to deductive arguments. They can also distinguish themselves as well educated individuals if they refer to inductive arguments ranking somewhere from of most improbable to most probable. It is also apparent after our study of Part One that validity cannot possibly apply to inductive arguments for the simple reason that inductive arguments do not arrive at their conclusion through the logical necessity of ‘entailment.’ They only promise a ‘probability’ for the conclusion. We will consider the nature of inductive arguments here in Part Two: Argument, and in Part Three: Refutation. It is sufficient to state here that premises for deductive arguments often arise from inductive reasoning about the ‘probable’ or ‘likely’ truth of those premises. For practical purposes there is a limit to the number of times that one can perform an inductive observation. Sufficient numbers of inductive instances lead ultimately to a hypothesis often stated as All X are Y, No X is Y, Some X is Y Some X is not Y. As we shall see, these are the building blocks of categorical syllogistic reasoning. A reciprocal relationship then exists between deductive and inductive arguments. The premises of deductive arguments are subject to inductive verification. That relationship will become more apparent in this section, as we continue through deductive arguments used in Categorical Logic, also known as Aristotelian Logic, and then to Induction and Propositional Logic at the end of Part Two. This basic training in the reciprocity between deductive and inductive reasoning will enhance your critical thinking skills for Part Three and the ‘crown jewel’ of rational thought, i.e., refutation. First, we consider a very brief history of Categorical Logic starting with understanding the nature of a ‘categorical reasoning’. This brief history will help us understand the nature of a categorical ‘term’, a categorical ‘proposition’. This will prepare us to then understand the structure and function of a categorical ‘syllogism’. Then we can learn how to build Categorical Syllogisms to produce valid argument structures on any topic in any academic discipline. 46 47 Part Two: Argue 48 Section 2 Categorical Logic Aristotle (384-322 B.C.) did not invent the science of logic. He did not even discover its basic laws, principles, ideas, or methods. But Aristotle’s name is forever associated with the oldest and most influential system of logic used in western culture for over 2,000 years. Why? Aristotle codified logic from the knowledge of those who went before him. Entering Plato’s (427-347 B.C.) Academy at the age of 17, Aristotle not only conceptually equaled his master, but eclipsed him in the codification of entire systems of thought including logic. As the foremost student of the Academy, Aristotle had access to the writings, teaching, and conceptual development of all the leading mathematics and philosophy prior to his time. Yet all this ancient knowledge and development of logical reasoning through formal mathematical systems was scattered throughout prior works. Aristotle surveyed and codified these into a series of six tracts which ancient and medieval commentators called the Organon, now understood as Categorical Logic. In these tracts Aristotle brought together all the reasoning insights from Thales (c.630c.550), Pythagoras (c.569) Anaximenes, (fl. c.546), Anaxagoras (c.500-c.428), Zeno (c.490-c.430), and Democritus (c.460-370), together with the teachings of his mentor Plato, and his contemporary, Heraclitus (c. 390c.322). The six Aristotelian tracts comprising The Organon are separately titled: Interpretation Categories Topics Prior Analytics Posterior Analytics On Sophistical Refutations Taken together, the collection was a driving force, not only for Euclid (c. 295), and Archimedes (287212), but for the entire history of philosophy and mathematics in western civilization till the early 1900’s. This extraordinary influence justifies our thorough study of Aristotelian logic. Thanks to the Internet Classics Archive, diligent 49 Student can read English translations of these primary sources online @ http://classics.mit.edu/Browse/index.html. Realizing that logic is the science of reasoning, Aristotle laid out his logical principles scientifically, as he did in so many other sciences. As is our custom, we begin this section with a few simple but precise definitions necessary to read and understand what follows in our study of argumentation. Categorical Term: any term that refers to a set or class of things, real or imaginary, that share unique, identifying attributes distinguishing members of that set or class from members of all other sets or classes. We call these attributes ‘class defining’ attributes. Example: The category ‘mammal’ is distinctly identified by the attribute ‘animals that breast feed their young’. (See the literal the meaning of the term ‘mammalian glands’) Categorical Logic: any study of necessary inferences infer-rules, forms, and principles between propositions that relate two classes or sets and their members, known as categories. Example: No foods served at ‘Mom’s’ are greasy meals. Some pizzas are greasy meals. Some foods served at ‘Mom’s’ are not pizzas. Standard Form Categorical Propositions: a n y proposition used in Categorical Logic having only five elements expressing: Quantity = All or only some category members Quality = Affirmative or negative truth claim Copula = Some form of the verb ‘to be’ Subject term = Categorical term before the copula Predicate term = Categorical term after the copula Examples: All animals are mammals Some animals are mammals No animals are mammals 50 Some animals are not mammals Syllogism: any two premises, single conclusion, deductive argument. Example: If win the Mega Lotto, then I’m rich. I win the Mega Lotto. Therefore, I’m rich. Standard From Categorical Syllogism: any two premise, single conclusion, deductive argument where all the propositions are standard form categorical propositions. Example: All Mega Lotto winners are rich people. No poor people are rich people. Therefore, no poor people are Mega Lotto winners. Contraries: Two propositions are contraries if both of them cannot be true at the same time, but both can be false at the same time. Example: Consider two propositions, All psychiatrists are insane people (and) No psychiatrists are insane people. Obviously, both of these claims cannot be true at the same time. However, it may be the case that both of them are false at the same time since it may be the case that: Some psychiatrists are not insane people. (or) Some psychiatrists are insane people. Contradictories: Two propositions are contradictories if both cannot be true, and both cannot be false at the same time. Example: consider these two propositions: All psychiatrists are insane people. (and) Some psychiatrists are not insane people. Obviously, the truth or falsity of one entails the truth or falsity of the 51 other. They cannot both be true, and they cannot both be false because one is the negation of the other. Universal Affirmative Categorical Propositions: any proposition that claims something about ALL members of a category. (See examples above.) Universal Negative Categorical Propositions: any proposition that denies something about ALL members of a category. (See examples above.) Particular Affirmative Categorical Propositions: any proposition that claims something about only SOME members of a category. (See examples above.) Particular Negative Categorical Propositions: any proposition that denies something about only SOME members of an entire category. (See examples above.) In even simpler terms, while there are many members of the category ‘animal,’ only some of them are mammals, and all of those some share the unique attribute of breast feeding their offspring. In other words, not all animals are mammals, only some are. In logic the word some means ‘at least one’, and the word all means ‘every one without exception.’ This is an important fact for beginning Categorical Logic students to fully understand. Certainly there are other words used in other systems of logic and reasoning to express partial membership in a category, class or set, but these words are easily translated into all, some, or none. Examples: ‘Most’ translates to some in Categorical Logic since it does not mean all. The same is true for expressions such as: ‘nearly all’, ‘the majority of all’, ‘practically all’, ‘almost all’, ‘not all’, etc. For the logician, all of these terms are synonymous with SOME. Likewise, expressions such as ‘entire,’ ‘complete,’ ‘total,’ ‘every,’ and ‘whole,’ etc., are synonymous with ALL. 52 Why this is an important fact to absorb in understanding how logic is the science of reasoning will become apparent as we examine the exact logical implications of category defining attributes in Categorical Logic. It is sufficient to note that there can be no strict ‘entailment,’ no ‘logical necessity,’ without clear, precise, and exact meanings of the universal term all, and the particular term some when composing propositions about members of class, sets, or categories. A claim about ‘most’ is not a claim about ‘all’. We hear claims on important matters everyday that illustrate this important logical distinction. For example, is it the case that ‘most’ global warming is caused by human technology or is it the case that ‘all’ global warming is caused by human technology? Arguments that claim ‘all’ have a high burden of proof. A single exception can weaken such an argument. Conversely, an argument claiming ‘some’ can mean anything from one to ‘almost all’. Which is it? Which argument form do we have sufficient evidence to claim? Will we be easily refuted if we choose the argument form with insufficient evidence? We tackle that problem in Part Three: Refutation. From these simple observations, and definitions we are now ready to advance our understanding of categorical argumentation. We next study how Aristotle constructs his entire logic system from just four basic kinds of propositions about categories, their members, and the logical inferences that can be reasoned between them. In so doing, we take up the study of a practice of argumentation that has been analyzed, tested, proven, and endured in western culture for nearly two thousand years. Now that we generally understand the basic ideas of a categorical, term, a categorical proposition, and the idea of a categorical syllogism used in Categorical Logic we can proceed to the necessary inferences that can be made from categorical propositions. As we will see in the next section, a necessary inference is a step from one idea to another idea without any intermediary idea being necessary to make that step. 53 Section 3 Categorical Propositions Not all sentences are propositions. However, every sentence or sentence fragment that states a claim is a proposition. However, only some propositions are categorical. Aristotle observed that all categorical propositions can be reduced to just four types, divided by only two elements: Quantity (number, all or some), and Quality (affirmative or negative). From these divisions Aristotle generated the four basic types of categorical propositions that are the foundation for his entire logic system. Simply using the two categories of animals and humans, here are those four basic categorical propositional types. Universal affirmative: All animals are mammals Particular affirmative: Some animals are mammals Universal negative: No animals are mammals Particular negative: Some animals are not mammals These four categorical proposition Types exhaust all logically possible relations between members of these two (or any) categories, as Aristotle reasoned. Alert students will notice immediately that only two of these four categorical propositions are true, based on scientific observations of animals and mammals: Some animals are mammals (particular affirmative) Some animals are not mammals (particular negative) The other two, the universal affirmative and the universal negative, we know are false from scientific observations. A categorical proposition, then, affirms or negates, in whole or in part (all or some), that members of one category are included or excluded as members of another category. Aristotle identified each of these propositional Types as the four most basic in categorical reasoning. It is believed that medieval scholars assigned the letters A, E, I, or O to these four Types from the Latin words AffIrmo meaning to affirm, and NEgO meaning to negate. Type A. universal affirmative proposition states that every member of one class is also a member of the second class. 54 55 Example: All humans are mortal animals. Type E. universal negative proposition states that no member of one class is also a member of the second. Example: No humans are mortal animals. Type I. particular affirmative proposition states that some members of one class are members of the second. Example: Some humans are mortal animals. Type O. particular negative proposition states that some members of one class are not members of the second. Example: Some humans are not mortal animals. The concept that members of one category are included or excluded by all or some members of another category is called distribution. This notion of distribution is the most essential power in Categorical (Aristotelian) Logic; in fact, it is the very analytic power of deductive validity itself. Distribution may be seen then as the very engine of logical entailment, and it rests on just three fundamental Laws of Thought. Here is Aristotle's formulation. The Law of Identity A thing is what it is. A = A The Law of Non-Contradiction A thing cannot be and not be at the same time and in the same respect. A does not equal not A The Law of Excluded Middle A thing either is or it is not. Between A and not A there is no middle term Applied to truth claim propositions: Law of identity = A is A This tautology (a statement equivalent to itself) forms the basis for all logic. Law of non-contradiction = Nothing can be itself and not be itself at the same time in exactly the same sense: A is., and not A is not cannot both be true at the same time. Or in Aristotle’s words, one cannot say of something that it is, and that it is not in the same respect, and at the same time. Law of the excluded middle: For any proposition either that proposition is true or its negation is true. Between A and/or not A there is no third possibility. It is not logically possible that there should be anything 56 between the two parts of a contradiction. Given the nature of philosophical inquiry it’s not surprising that many attempts have been made to refute these three Laws of Thought without invoking them in the very act of arguing against them. Aristotle himself is thought to have placed some limits on the laws of thought that he codified from earlier thinkers like Parmenides. Clearly a thing cannot be both ‘green’ and ‘not green’ at the same time and in the same respect. But this may be attributable more to the construct of human perception than to the world of ‘green’ or ‘not green’ things. “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.” (Metaphysics G, 3,1005b18-20) Aristotle seems to warn against imposing the three laws of thought that order thinking on the natural world of things, events and their attributes. So the debate goes. For our purpose, there is little or no debate about the irrefutability of these three laws without involving a contradiction. That of course does not mean there is no sound refutation of these three laws. It just makes it virtually impossible to imagine how such a refutation could be construed without employing them Since the first law, the law of identity is a tautology, i.e., a statement equivalent to itself; it is not arguable without uttering an absurdity. The second, the law of non-contradiction, is also unarguable without actually using the law itself to refute it. To do so is to present a contradiction resulting in yet another absurdity. One cannot prove it either without begging-the-question. As for the third, the law of the excluded middle, it follows necessarily from the first two. For if everything that is, is, and if it cannot both be the case that something is, and that something is not, then it follows of necessity that between A is, and A is not, no logical middle option is possible. Therefore, to master classical deductive logic, the following precise definition must be fully understood. This definition is precise in the sense that it tells us exactly what distribution is, and precisely what it is not. A categorical term is distributed if, and only if, the categorical proposition that contains it tells us something about ALL members of 57 that categorical term. Conversely, a categorical term is undistributed if, and only if, the categorical proposition that contains it does NOT tell us something about ALL members of that categorical term. You will want to commit this definition to memory. You will apply it constantly in your full understanding of categorical argumentation. As previously stipulated, Categorical Propositions are said to have quality (either affirmative or negative), and quantity (either universal or particular) and that they have distributed and/or undistributed categorical terms. Again, a proposition is said to distribute a term if that proposition refers to all members of the class designated by the term. The following chart illuminates the ways in which A, E, I, and O type propositions either distribute, or do not distribute their subject and/or predicate terms. You should also commit this chart to memory as a visual companion to your working definition of distribution. Quantity & Quality Type Standard From Distribution of Terms A All S is P Universal Affirmative E No S is P Universal Negative I Some S is P Particular Affirmative Neither Subject nor Predicate distributed O Some S is not P Particular Negative Only Predicate distributed Subject distributed Predicate not distributed Both Subject and Predicate distributed The reason for the emphasis on Predicate term is distributed for Type O categorical propositions is because most students fail to see why this is the case. How does a proposition like, Some pizzas are NOT greasy things, tell us something about ALL greasy things? The answer is simple to understand if you read the proposition in its full logical exactitude. Some pizzas are not greasy things. Literally means in logic: There exists at least one thing called a pizza, and that one thing called a pizza is not included in the entire category of greasy things. So, in logical terms, all Type O categorical propositions do in fact distribute the predicate term. This is another vital point to grasp. Using these four basic Types of categorical propositions, Aristotle is able to construct a square to graphically illustrate the several ways these propositions can be opposed to one another. The traditional square of opposition, shown below, 58 graphically displays the opposing relationships that exist between the four different categorical proposition types. When S and P are used for subject and predicate terms in the propositions, they are said to be opposed to each other in any of six ways: 1. 2. 3. 4. 5. 6. All S is P, and Some S is not P are contradictories. No S is P, and Some S is P are contradictories. All S is P, and No S is P are contraries. Some S is P, and Some S is not P are subcontraries Some S is P, is the subaltern of All S is P Some S is not , is the subaltern of No S is P Opposition by propositional Type yields: Types A and E are contraries Types I and O are subcontraries Types A and O are contradictories Types E and I are contradictories Type I is the subaltern of Type I Type O is the subaltern of Type E (Note: The modern interpretation of the traditional Aristotelian Square of Opposition only recognizes Contradictions as being opposed to each in the strictest logical sense. This is so because Contrary propositions A & E can both be false at the same time and Subcontrary propositions I and O can both be true at the same time thus they are not strictly opposed to each other as contradictions are except under very limited conditions. 59 Now we are ready to make sense of the graphic below depicting the Traditional (Aristotelian) Square of Opposition for all four Types of Standard Form Categorical Propositions. As noted, you may find that the square of opposition in some contemporary logic texts appears quite different. While contradictories are accepted by most modern logicians, contraries, subcontraries and subalterns are not. In modern logic text books, the traditional square of opposition is reduced to something like the following diagram. Why is this? The answer revolves around the philosophical debate among modern logicians about the very nature of Categorical Terms, and the Universal and Particular Categorical Propositions that relate them. Simply stated, if all categorical terms were to refer to classes, sets, or categories of members that actually exist, then there would be no debate about the existential import of such terms and their propositions. Modern logicians debate this existential import question. While our concern as critical 60 thinkers is not the same as that of the professional logician, nevertheless the point does need clarification. In mathematics, literature, and even science, we often refer to sets, classes, and categories of things that are purely imaginary or theoretical. The empty set in mathematics, the unicorn in literature, the black hole in astrophysics, the string of contemporary physics; these, and many others, are examples of categories that we imagine to have members, yet lack direct experience that such things actually exist. Are we then prevented from using categorical logic to reason about these empty categories? Certainly we are not. There is a simple and effective way to rescue the traditional square of opposition from this criticism of modern logicians. We just stipulate, when referring to any category, that we refer to things either real or imagined. As we will be see in the section on Definitions, in Part Three: Refutation to ‘stipulate’ simply means to ‘accept as agreed’. Opposing lawyers in court often stipulate to facts of the case at trial. Mathematicians stipulate sets with no members to work out proofs. Writers stipulate imaginary worlds and creatures in their poems and novels. Scientists stipulate hypothetical laws, principles, forces, powers, and substances when endeavoring to explain events which elude existing theories. Applying the three basic laws of thought, then, to sets, classes, and categories with no members is not hindered. We can continue to reason through categorical arguments provided we stipulate that if categorical terms had any members, even hypothetical ones, then the principles of categorical logic apply. We adopt this stipulation here. Three more ideas are introduced in this section to complete our understanding of the power in categorical propositions around the square of opposition. These ideas are; conversion, obversion and contraposition. Each are instances of immediate inferences. An immediate inference is a necessary mental progression from one proposition to another without any other proposition being needed in the process. Example: If any Type A proposition is factually true, then its contradictory Type O proposition must be factually false by immediate inference. Two useful and often used instances of immediate inference in 61 categorical logic are conversion and obversion. Contraposition is of interest to those with a fondness for logical structures but is seldom used in ordinary discourse. Nevertheless, it is introduced here for completeness of immediate inferences that can be drawn, in some instances, from A E I and O categorical propositions. Conversion: swapping the position of the subject and predicate terms in any standard form categorical proposition. (Valid immediate inference only for Type E and Type I categorical propositions) Examples: No S is P converts to No P is S Some S is P converts to Some P is S Obversion: changing the Quality of the proposition, and replacing the predicate term with its complement (everything other than that term signified by placing non before that term).Obversion is a valid immediate inference for all Type A, E, I, and O categorical propositions. Examples: A All S is P. obverts to Type E No S is not-P. E No S is P. obverts to Type A All S is not P. I Some S is P obverts t0 Type 0 Some S is not not-P 0 Some S is not P. obverts to Type I Some S is not-P. The reason we would want to convert and/or obvert any standard form categorical proposition is to observe if an immediate inference can be validly derived from the outcome. When we walk around the square of opposition, applying conversion to each of the propositional types (A, E, I, & O), we discover something very interesting. We learn that, while conversion of a Type A and Type O proposition does not produce reciprocally true/false results, conversion of Type E and Type I propositions does in fact produce reciprocally true/false results. Examples: All S is P does not entail that All P is S by conversion immediate inference. 62 Some S is not P does not entail that Some P is not S by conversion immediate inference. But No S is P does entail that No P is S by conversion immediate inference. And Some S is P does entail that Some P is S by conversion immediate inference. You may have noticed quickly that Type E propositions distribute both subject and predicate terms, while Type I propositions distribute neither subject nor predicate term. The reason lies in the very precise definition we previously gave for the term distribution. Ordinary language examples, then, show the obverse of ‘All ants are insects’ is ‘No ants are noninsects’; the obverse of ‘No fish are mammals’ is ‘All fish are nonmammals’; the obverse of ‘some musicians’ are males is ‘some musicians are not nonmales’; and the obverse of ‘some cars are not sedans’ is ‘some cars are nonsedans’. In this way, obverting a proposition gives us a logical equivalent of the original proposition before obversion is performed. Obversion is the only immediate inference that is valid for all four categorical propositions, Types, A, E, I, and O. In each of the instances cited above, the original proposition and its obverse will have exactly the same truth value regardless if it turns out to be true or false. Not only do the immediate inferences provided by conversion and obversion serve our understanding of the notion of distribution in categorical logic, they are useful in developing our refutation skills, as presented in Part Three. They reveal logical exactitude. For instance, just because someone is a nonhero, that someone is not necessarily a coward. Knowledge of obversion reveals this exact meaning. Equally useful is the understanding by conversion that while it may be the case that, All democratic ideals are ideals good for corporations, it does not follow that, All ideals good for corporations are good for democratic ideals. Contraposition: is formed as a combination of conversion and 63 obversion. To form the contrapositive of a categorical proposition these steps are taken; • Switching the subject and predicate terms, as in taking the converse Replacing both the subject and the predicate terms with their complements • • The quality and quantity of the proposition remain as they were. It is always valid to infer the contrapositive of an A proposition. An A proposition says that the class of S is included within the class of P. So anything outside the class of P (i.e., all the non-P) must be outside the class of S (i.e., it must be a non-S). Example: Boston is in America, so if you're not in America, you're not in Boston. While being in America is a necessary condition for being in Boston it is not a sufficient condition. Contraposition is not a valid immediate inference for I and E propositions. Examples: The E proposition, "No primate is an aquatic animal," is clearly not equivalent to its contrapositive, "No nonaquatic animal is a nonprimate," because the first is true and the second false (cows are nonaquatic animals but they are nonprimates). Similarly, the I proposition, "Some soldiers are nonofficers," is clearly not equivalent to its contrapositive, "Some officers are nonsoldiers." Besides the type A proposition the type O proposition is the only other type that is equivalent to its contrapositive. The true value of mastering these immediate inferences is knowing how and when they fail validity. The art of refutation presented in Part Three here will demonstrate the usefulness of pointing out that just because a person is not a hero that does not entail by immediate inference that the person is a coward. Yet this false inference is very often made in popular speech. However, before we can refute arguments we must first build them. We must learn their form and their structure. Following this is the formal study of the most powerful form of 64 argument, the categorical syllogism. 65 Section 4 Categorical Syllogisms The categorical syllogism is a very simple form of argument. It harnesses the ‘power of distribution’ to generate a conclusion from only two categorical premises with absolutely certain validity because the ‘form’ of the four types of categorical propositions, A, E, I, & O, express either category inclusion or exclusion of members in one class with members of another class. Utilizing the power of distribution is precisely what happens in the argument structure known as a Standard Form Categorical Syllogism. ‘Validity’ then, is un...
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Running head: SOLUTIONS TO ILLEGAL IMMIGRATION

Solutions to Illegal Immigration
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SOLUTIONS TO ILLEGAL IMMIGRATION

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Today 13% of the population in the United States is made of immigrants. There are 11.3
million immigrants in the US which is a decrease from 12.2 million recorded in 2007. This can
be attributed to the measures that have been put in place to discourage immigration into the
country and also deal with the illegal immigrants who have infiltrated the country (Lee, Ottati &
Hussain, 2001). Pathway to citizenship also referred to as amnesty and is a process through
which illegal immigrants go through to be identified as citizens of a country. The immigrants
become naturalized citizens. They can enjoy the full benefits of being an American citizen. There
has been a heated debate in the United States on how the illegal immigrants should be dealt with.
Some citizens perceive that the illegal migrants pose a burden to the right country's population
and the limited resources together with job opportunities are divided including undeserving
individuals. This paper will discuss how the issue of resident illegal immigrants in the United
States can be solved through a pathway to citizenship rather than deportation or other punitive
measures.
Those in favor of a path to citizenship argue that illegal immigrants have many benefits
to the economy. This is as opposed to the common perception that the immigrants take job
opportunities created and meant for the American citizens what is commonly referred to as
‘stealing their jobs.' These allegations are false as the immigrants only work in areas that are
unpopular among the American population but are essential for a smooth running of the
economy (Hanson, 2010). These job opportunities are mostly the one that requires the low end of
the skill spectrum, e.g., farming, waiting on tables and cleaning just to name a few. The tasks are
always considered to be trivial since no special skill is required and the most American are not
willing to be associated with them, and if some engage in them, they tend to demand
overwhelming charges. The immigrants, unlike the accredited citizens, offer their labor effort at

SOLUTIONS TO ILLEGAL IMMIGRATION

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a relatively lower cost. This bene...


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